SciELO - Scientific Electronic Library Online

 issue51Influence of the Binomial Crossover in the DE Variants Based on the Robot Design with Optimum Mechanical EnergyClassification of Group Potency Levels of Software Development Student Teams author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO



On-line version ISSN 1870-9044

Polibits  n.51 México Jan./Jun. 2015 

The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters


Leanderson André and Rafael Stubs Parpinelli


The authors are with the Graduate Program in Applied Computing, Departament of Computer Science, State University of Santa Catarina, Joinville, Brazil. (e-mail:,


Manuscript received on January 20, 2015,
Accepted for publication on March 8, 2015,
Published on June 15, 2015.



In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (ABDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The ABDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (AGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (AIGA). The results show that ABDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.

Key words: Adaptive parameter control, binary differential evolution, multiple knapsack problem, evolutionary computation.





[1] M. Vasquez, J.-K. Hao et al., "A hybrid approach for the 0-1 multidimensional knapsack problem," in IJCAI, 2001, pp. 328-333.         [ Links ]

[2] A. Freville, "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, vol. 155, no. 1, pp. 1-21, 2004.         [ Links ]

[3] J. C. Bansal and K. Deep, "A modified binary particle swarm optimization for knapsack problems," Applied Mathematics and Computation, vol. 218, no. 22, pp. 11 042-11 061, 2012.         [ Links ]

[4] M. A. K. Azad, A. M. A. Rocha, and E. M. Fernandes, "Improved binary artificial fish swarm algorithm for the 0-1 multidimensional knapsack problems," Swarm and Evolutionary Computation, vol. 14, pp. 66-75, 2014.         [ Links ]

[5] L. Wang, X. long Zheng, and S. yao Wang, "A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem," Knowledge-Based Systems, vol. 48, no. 0, pp. 17-23, 2013.         [ Links ]

[6] R. Storn and K. Price, "Differential evolution : A simple and efficient heuristic for global optimization over continuous spaces," J. ofGlobal Optimization, vol. 11, no. 4, pp. 341-359, Dec. 1997.         [ Links ]

[7] K. De Jong, Evolutionary Computation: A Unified Approach, ser. Bradford Book. Mit Press, 2006.         [ Links ]

[8] X.-S. Yang, "Chapter 6—differential evolution," in Nature-Inspired Optimization Algorithms. Oxford: Elsevier, 2014, pp. 89-97.         [ Links ]

[9] J. Krause, J. Cordeiro, R. S. Parpinelli, and H. S. Lopes, "A survey of swarm algorithms applied to discrete optimization problems," Swarm Intelligence and Bio-inspired Computation: Theory and Applications. Elsevier Science & Technology Books, pp. 169-191, 2013.         [ Links ]

[10] J. Krause, R. S. Parpinelli, and H. S. Lopes, "Proposta de um algoritmo inspirado em evolucao diferencial aplicado ao problema multidimensional da mochila," Anais do IX Encontro Nacional de Inteligencia Artificial—ENIA. Curitiba, PR: SBC, 2012.         [ Links ]

[11] A. Eiben, R. Hinterding, and Z. Michalewicz, "Parameter control in evolutionary algorithms," IEEE Transactions on Evolutionary Computation, vol. 3, no. 2, pp. 124-141, Jul 1999.         [ Links ]

[12] L. Andre and R. S. Parpinelli, "Controle de parámetros em inteligencia de enxame e computacao evolutiva," Revista de Informática Teórica e Aplicada, vol. 21, no. 2, pp. 83-128, 2014.         [ Links ]

[13] D. Thierens, "An adaptive pursuit strategy for allocating operator probabilities," in Proceedings of the 2005 conference on Genetic and evolutionary computation. ACM, 2005, pp. 1539-1546.         [ Links ]

[14] A. Fialho, L. Da Costa, M. Schoenauer, and M. Sebag, "Extreme value based adaptive operator selection," in Parallel Problem Solving from Nature—PPSN X. Springer, 2008, pp. 175-184.         [ Links ]

[15] A. Aleti and I. Moser, "Studying feedback mechanisms for adaptive parameter control in evolutionary algorithms," in IEEE Congress on Evolutionary Computation (CEC), June 2013, pp. 3117-3124.         [ Links ]

[16] O. Kramer, "Evolutionary self-adaptation: a survey of operators and strategy parameters," Evolutionary Intelligence, vol. 3, no. 2, pp. 51-65, 2010.         [ Links ]

[17] L. Andre and R. S. Parpinelli, "An island-inspired genetic algorithm with adaptive parameters applied to the multiple knapsack problem," in Proceedings of the 5th International Conference on Metaheuristics and ature Inspired Computing, October 2014, pp. 1-2.         [ Links ]

[18] A. Hoff, A. L0kketangen, and I. Mittet, "Genetic algorithms for 0/1 multidimensional knapsack problems," in Proceedings Norsk Informatikk Konferanse. Citeseer, 1996, pp. 291-301.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License